What is 5/2 ln(5)+5/2 ln(2) ?

The solution to 5/2 ln(5)+5/2 ln(2) is ln(100sqrt(10))

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simplify 5/2 ln(5)+5/2 ln(2)

simplify

\frac{5}{2} ln (5) + \frac{5}{2} ln (2)

ln (10010)

Decimal Notation

5.75646 \dots

Solution steps

\frac{5}{2} ln (5) + \frac{5}{2} ln (2)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{5}{2} ln (5) = ln (5^{\frac{5}{2}})

= ln (5^{\frac{5}{2}}) + \frac{5}{2} ln (2)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{5}{2} ln (2) = ln (2^{\frac{5}{2}})

= ln (5^{\frac{5}{2}}) + ln (2^{\frac{5}{2}})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (5^{\frac{5}{2}}) + ln (2^{\frac{5}{2}}) = ln (5^{\frac{5}{2}} \cdot 2^{\frac{5}{2}})

= ln (5^{\frac{5}{2}} \cdot 2^{\frac{5}{2}})

5^{\frac{5}{2}} \cdot 2^{\frac{5}{2}} = 10010

= ln (10010)

\frac{ln ( 0.15 ) - ln ( 0.25 )}{- 6.7 \cdot 1 0 ^{- 4}}

3 lo g_{m} (z) - \frac{1}{5} lo g_{m} (w) + 6 lo g_{m} (x)

x^{l o g_{x} ((x + 3)^{2}) = 16}

ln (a) + 2 ln (b)

ln (x) - ln (1 - x)

What is 5/2 ln(5)+5/2 ln(2) ?
The solution to 5/2 ln(5)+5/2 ln(2) is ln(100sqrt(10))